In speech encoding, transform encoding whereby a time signal is transformed into a frequency domain and transform coefficients are encoded, can efficiently eliminate redundancy contained in the time domain signal. In addition, in the transform encoding, by utilizing perceptual characteristics represented in the frequency domain, it is possible to implement encoding in which quantization distortion is difficult to be perceived even at a low bit rate.
In transform encoding for the recent years, a transform technique called lapped orthogonal transform (LOT) is often used. In LOT, transform is performed based on an orthogonal function taking into consideration not only the orthogonal components within a block but also the orthogonal components between adjacent blocks. Typical techniques of such transform include MDCT (Modified Discrete Cosine Transform). In MDCT, analysis frames are arranged so that a current analysis frame overlaps previous and subsequent analysis frames, and analysis is performed. At this time, it is only necessary to encode coefficients corresponding to half of the analysis length out of transformed coefficients, so that efficient encoding can be performed by using MDCT. In addition, upon synthesis, the current frame and its adjacent frames are overlapped and added, thereby providing a feature that even under circumstances where different quantization distortions occur for each frame, discontinuity at frame boundaries is unlikely to occur.
Normally, when analysis/synthesis is performed by MDCT, a target signal is multiplied by an analysis window and a synthesis window which are window functions. The analysis window/synthesis window to be used at this time has a slope at a portion to be overlapped with the adjacent frames. The length of the overlapping period (that is, the length of the slope) and a delay necessary for buffering an input frame correspond to the length of a delay occurring by the MDCT analysis/synthesis. If this delay increases in bidirectional communication, it takes time for a response from a terminal to arrive at the other terminal, and therefore smooth conversation cannot be performed. Thus, it is preferable that the delay is as short as possible.
Conventional MDCT will be described below.
When a condition expressed by equation 1 is satisfied, the analysis window/synthesis window to be used in MDCT realizes perfect reconstruction (where distortion due to transform is zero on the assumption that there is no quantization distortion).
                                                                                          w                                      i                    ⁢                                                                                  ⁢                    n                                                  ⁡                                  (                  i                  )                                            ·                                                w                  out                                ⁡                                  (                  i                  )                                                      +                                                            w                                      i                    ⁢                                                                                  ⁢                    n                                                  ⁡                                  (                                      i                    +                                          N                      /                      2                                                        )                                            ·                                                w                  out                                ⁡                                  (                                      i                    +                                          N                      /                      2                                                        )                                                              =          1                ⁢                                  ⁢                  (                      0            ≤            i            <            N                    )                                    (                  Equation          ⁢                                          ⁢          1                )            
As a typical window satisfying the condition of equation 1, Non-Patent Document 1 proposes a sine window expressed by equation 2. The sine window is as shown in FIG. 1. When such a sine window is used, side lobes are sufficiently attenuated in the spectrum characteristics of the sine window, so that accurate spectrum analysis is possible.
                                          w            ⁡                          (              i              )                                =                      sin            ⁡                          (                                                i                  ⁢                                                                          ⁢                  π                                N                            )                                      ⁢                                  ⁢                  (                      0            ≤            i            <            N                    )                                    (                  Equation          ⁢                                          ⁢          2                )            
Non-Patent Document 2 proposes a method of performing MDCT analysis/synthesis using the window expressed by equation 3 as a window satisfying the condition of equation 1. Here, N is the length of the analysis window, and L is the length of the overlapping period. The window expressed by equation 3 is as shown in FIG. 2. When such a window is used, the overlapping period is L, and thus the delay by this window is represented by L. Therefore, the occurrence of the delay can be suppressed by setting overlapping period L short.
                              w          ⁡                      (            i            )                          =                  {                                                                                          0                    ⁢                                                                                  ⁢                    0                                    ≤                  i                  <                                                                                    1                        4                                            ⁢                      N                                        -                                                                  1                        2                                            ⁢                      L                                                                                                                                                                                                              cos                        ⁡                                                  (                                                                                    π                              ·                                                              (                                                                  i                                  -                                                                      N                                    /                                    4                                                                    -                                                                      L                                    /                                    2                                                                                                  )                                                                                                                    2                              ⁢                              L                                                                                )                                                                                                                                                                                                                        1                              4                                                        ⁢                            N                                                    -                                                                                    1                              2                                                        ⁢                            L                                                                          ≤                        i                        <                                                                                                            1                              4                                                        ⁢                            N                                                    +                                                                                    1                              2                                                        ⁢                            L                                                                                                                                                                                                                                                                                      1                        ⁢                                                                                                  ⁢                                                  1                          4                                                ⁢                        N                                            +                                                                        1                          2                                                ⁢                        L                                                              ≤                    i                    <                                                                                            3                          4                                                ⁢                        N                                            -                                                                        1                          2                                                ⁢                        L                                                                              ⁢                                                                                                                                                                                                                                cos                        ⁡                                                  (                                                                                    π                              ·                                                              (                                                                  i                                  -                                                                      3                                    ⁢                                                                          N                                      /                                      4                                                                                                        +                                                                      L                                    /                                    2                                                                                                  )                                                                                                                    2                              ⁢                              L                                                                                )                                                                                                                                                                                                                        3                              4                                                        ⁢                            N                                                    -                                                                                    1                              2                                                        ⁢                            L                                                                          ≤                        i                        <                                                                                                            3                              4                                                        ⁢                            N                                                    +                                                                                    1                              2                                                        ⁢                            L                                                                                                                                                                                                                                                              0                      ⁢                                                                                          ⁢                                              3                        4                                            ⁢                      N                                        +                                                                  1                        2                                            ⁢                      L                                                        ≤                  i                  <                  N                                                                                        (                  Equation          ⁢                                          ⁢          3                )                Non-Patent Document 1: Takehiro Moriya, “Speech Coding”, the Institute of Electronics, Information and Communication Engineers, Oct. 20, 1998, pp. 36-38    Non-Patent Document 2: M. Iwadare, et al., “A 128 kb/s Hi-Fi Audio CODEC Based on Adaptive Transform Coding with Adaptive Block Size MDCT,” IEEE Journal on Selected Areas in Communications, Vol. 10, No. 1, pp. 138-144, January 1992.